Ternary Egyptian fractions with prime denominator
Adva Mond, Julien Portier

TL;DR
This paper investigates the number of representations of fractions with prime denominators as sums of three unit fractions, providing improved bounds on their cumulative count over primes.
Contribution
It improves the upper bound on the sum of the counts of such representations for primes, refining previous estimates significantly.
Findings
Established a tighter upper bound: x (a0a0a0)^3 (a0a0)^2
Confirmed the asymptotic growth rate of the sum over primes
Enhanced understanding of Egyptian fractions with prime denominators
Abstract
For a prime number , let . In 2019 Luca and Pappalardi proved that . We improve the upper bound, showing .
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